The new primocane-fruiting blackberry cultivar called ‘APF-205T’ is described herein. The new cultivar originated from a hand-pollinated cross of Arkansas selections ‘APF-77’ (U.S. Plant Pat. No. 24,249) x ‘APF-49T’ (non-patented, unreleased genotype) made in 2005. The seeds resulting from this controlled hybridization were germinated in a greenhouse in the spring of 2006 and planted in a field near Clarksville, Ark. (West-Central Arkansas). The seedlings fruited in the summer of 2008 and one seedling, designated ‘APF-205T’, was selected. It was selected for its large fruit with consistent size and sweet flavor, thornless canes with consistently good plant health, and primocane-fruiting habit.